Weak values are the fundamental values for observables in a pre- and postselected system. Weak values are typically measured by weak measurement, in which weak values appear in the change of not the pre- and postselected system but the probe system. This indirect characteristic of weak measurement obscures the meaning of weak values for the pre- and postselected system, in contrast to conventional physical quantities, which have a clear operational meaning. In this study, we operationally formulate weak values as the sensitivity of postselection probability amplitude to small transformation in a pre- and postselected system. This formulation of weak values, which is free from the concept of probe shift assumed in weak measurement, gives a direct interpretation of strange weak values for the pre- and postselected system. Furthermore, this formulation can simplify weak-value measurement experiments because the associated measurements appearing in the modulus change of the postselection probability amplitude do not require external degrees of freedom.

We have theoretically developed a microscopy technique to visualize arbitrarily oriented single quantum fluorescent emitters with resolutions beyond the diffraction limit. The lateral resolution of 72 nm, the axial resolution of 103 nm, and the orientational independence degree of 0.9 have been demonstrated. The latter quantifies the dependence of the image intensity maximum of a single quantum emitter on the orientation of its transition dipole moment and can take on possible values from 0 to 1, where 1 corresponds to a completely excluded dependence and 0 indicates that the emitter is absolutely invisible at some orientations. The suggested method is based on orientational stimulated emission depletion microscopy. An elliptically polarized cylindrical vector Bessel beam is suggested as an excitation beam and an elliptically polarized vortex cylindrical vector Bessel beam with the topological charge $m=\pm 1$ as the depletion beam to deplete focal-plane fluorescence. A pair of linearly polarized cylindrical vector beams focused in a $4\pi$ microscope scheme is assumed to deplete out-of-focal-plane fluorescence. An image of a single quantum emitter can be recorded at four conjugated sets of polarizations of the beams, giving images with different intensity distributions but the same intensity maximum values, and the maximums depicted in the same plot form a rectangle from which one can derive the position and orientation of the emitter. The present study paves the way for super-resolution microscopy of arbitrarily oriented single molecules, which can enhance single molecule counting techniques, studies of polymer materials by guest-fluorescent-molecule probing, and similar applications.

The input-output formalism is the basis to study the response of an optical cavity to the external stimulations. The existing theories usually handle cavity systems with only one internal mode. However, there is growing interest in more complex systems, especially the hybrid cavity-matter systems, which contain at least two internal modes, one or more from both the optical cavity and the matter. Here we propose a graphical loop theory to calculate and visualize the reflection and transmission spectrum of such a multimode cavity, resembling the role of Feynman diagrams in the quantum field theory. This loop theory gives a unified picture to interpret the experimental observations of a hybrid magnet-light system and is extremely easy to apply to arbitrary complicated problems without any calculations.

The Einstein-Podolsky-Rosen (EPR) steering is an intermediate quantum nonlocality between entanglement and Bell nonlocality, which plays an important role in quantum information processing tasks. In the past few years, the investigations concerning the EPR steering have been demonstrated in a series of experiments. However, these studies rely on the relevant steering inequalities and the choices of measurement settings. Here, we experimentally verify the EPR steering via entanglement detection without using any steering inequality and measurement setting. By constructing two new states from a two-qubit state, we observe the EPR steering by detecting the entanglement of these new states. The results show that the entanglement of the newly constructed states can be regarded as an unusual kind of steering witness for these states. Compared to the results of Xiao et al. [Phys. Rev. Lett. 118, 140404 (2017)], we find that the ability to detect the EPR steering in our scenario is stronger than that of two-setting projective measurements, which can observe more steerable states. Hence, our demonstrations can deepen the understanding of the connection between the EPR steering and entanglement.

To gain better insight into the complexity theory of quantum annealing, we propose and solve a class of spin systems which contain bottlenecks of the kind expected to dominate the runtime of quantum annealing as it tries to solve difficult optimization problems. We uncover a noise amplification effect at these bottlenecks, whereby tunneling rates caused by flux-qubit noise scale in proportion to the number of qubits $\mathcal{N}$ in the limit that $\mathcal{N}\to \infty$. By solving the incoherent annealing dynamics exactly, we find a wide range of regimes where the probability that a quantum annealer remains in the ground state upon exiting the bottleneck is close to one-half. We corroborate our analysis with detailed simulations of the performance of the D-Wave 2X quantum annealer on our class of computational problems.

We develop an operator-based description of two types of multimode-entangled single-neutron quantum optical devices: Wollaston prisms and radio-frequency spin flippers in inclined magnetic-field gradients. This treatment is similar to the approach used in quantum optics, and is convenient for the analysis of quantum contextuality measurements in certain types of neutron interferometers. We describe operationally the way multimode-entangled single-neutron states evolve in these devices, and provide expressions for the associated operators describing the dynamics, in the limit in which the neutron state space is approximated by a finite tensor product of distinguishable subsystems. We design entangled-neutron interferometers to measure entanglement witnesses for the Clauser, Horne, Shimony, and Holt and Mermin inequalities, and compare the theoretical predictions with recent experimental results. We present the generalization of these expressions to $n$ entangled distinguishable subsystems, which could become relevant in the future if it becomes possible to add neutron orbital angular momentum to the experimentally accessible list of entangled modes. We view this paper as a necessary first step towards a theoretical description of entangled neutron scattering from strongly entangled matter, and we explain why it should be possible to formulate a useful generalization of the usual Van Hove linear-response theory for this case. We also briefly describe some other scientific extensions and applications which can benefit from interferometric measurements using the types of single-neutron multimode entanglement described by this analysis.

We consider an expansion of the strongly interacting superfluid Fermi gas in a vacuum in the so-called unitary regime when the chemical potential $\mu \propto {\hslash }^2{n}^{2/3}/m$, where $n$ is the density of the Bose-Einstein condensate of Cooper pairs of fermionic atoms. At low temperatures $T\to 0$, such an expansion can be described in the framework of the Gross-Pitaevskii equation (GPE). For such a dependence of the chemical potential on the density, the GPE has additional symmetries, resulting in the existence of the virial theorem, connecting the mean size of the gas cloud and its Hamiltonian. It leads asymptotically at $t\to \infty$ to the gas cloud expansion, linearly growing in time. We study such asymptotics and reveal the perfect match between the quasiclassical self-similar solution and the asymptotic expansion of the noninteracting gas. This match is governed by the virial theorem, derived through utilizing the Talanov transformation, which was first obtained for the stationary self-focusing of light in media with a cubic nonlinearity due to the Kerr effect. In the quasiclassical limit, the equations of motion coincide with three-dimensional hydrodynamics for the perfect monatomic gas with $\gamma =5/3$. Their self-similar solution describes, within the background of the gas expansion, the angular deformities of the gas shape in the framework of the Ermakov-Ray-Reid–type system.

Optomechanically induced transparency is an important quantum phenomenon in cavity optomechanics. Here, we study the properties of optomechanically induced transparency in the simplest optomechanical system (consisting of one cavity and one mechanical resonator) considering a nonlinear effect that was ignored in previous works. With the nonlinear effect, we find the ideal optomechanically induced transparency dip can be easily achieved, and the width of the optomechanically induced transparency dip can become very narrow especially in the unresolved sideband regime. Finally, we study the properties of optomechanically induced gain, and give the analytic expression about the maximum value of gain.

We study the protective measurement of a qubit by a second qubit acting as a probe. Consideration of this model is motivated by the possibility of its experimental implementation in multiqubit systems such as trapped ions. In our scheme, information about the expectation value of an arbitrary observable of the system qubit is encoded in the rotation of the state of the probe qubit. We describe the structure of the Hamiltonian that gives rise to this measurement and analyze the resulting dynamics under a variety of realistic conditions, such as noninfinitesimal measurement strengths, repeated measurements, non-negligible intrinsic dynamics of the probe, and interactions of the system and probe qubits with an environment. We propose an experimental realization of our model in an ion trap. The experiment may be performed with existing technology and makes use of established experimental methods for the engineering and control of Hamiltonians for quantum gates and quantum simulations of spin systems.

We analyze the dynamics of a spin-$\frac{1}{2}$ subsystem coupled to a spin chain. We simulate numerically the full quantum many-body system for various sets of parameters and initial states of the chain, and characterize the divisibility of the subsystem dynamics, i.e., whether it is Markovian and can be described by a (time-dependent) master equation. We identify regimes in which the subsystem admits such Markovian description, despite the many-body setting, and provide insight about why the same is not possible in other regimes. Interestingly, coupling the subsystem at the edge, instead of the center, of the chain gives rise to qualitatively distinct behavior.

Quantum processes, such as quantum circuits, quantum memories, and quantum channels, are essential ingredients in almost all quantum information processing tasks. However, the characterization of these processes remains a daunting task due to the exponentially increasing amount of resources required by traditional methods. Here, by first proposing the concept of quantum process verification, we establish two efficient and practical protocols for verifying quantum processes which can provide an exponential improvement over the standard quantum process tomography and a quadratic improvement over the method of direct fidelity estimation. The efficacy of our protocols is illustrated with the verification of various quantum gates as well as the processes of well-known quantum circuits. Moreover, our protocols are readily applicable with current experimental techniques since only local measurements are required. In addition, we show that our protocols for verifying quantum processes can be easily adapted to verify quantum measurements.

Efficient verification of the functioning of quantum devices is a key to the development of quantum technologies, but is a daunting task as the system size increases. Here we propose a simple and general framework for verifying unitary transformations that can be applied to both individual quantum gates and gate sets, including quantum circuits. This framework enables efficient verification of many important unitary transformations, including but not limited to all bipartite unitaries, Clifford unitaries, generalized controlled-$Z$ gates, generalized controlled-not gates, the controlled-swap gate, and permutation transformations. For all these unitaries, the sample complexity increases at most linearly with the system size and is often independent of the system size. Moreover, little overhead is incurred even if one can only prepare Pauli eigenstates and perform local measurements. Our approach is applicable in many scenarios in which randomized benchmarking (RB) does not apply and is thus instrumental to quantum computation and many other applications in quantum information processing.

Looking inside a laser pulse by detecting an instantaneous ionization rate (IIR) has been a useful instrument for characterizing subcycle ionization dynamics [Phys. Rev. A 64, 013409 (2001)]. However, this instrument relies entirely on IIR being a deterministic function of time. By introducing an IIR operator and studying its autocorrelation function, we show that electron ionization dynamics is more complex and the ionization rate depends on the “prehistory,” i.e., the IIRs at the two instants of time are, in fact, correlated. The pattern of this correlation changes dramatically between the multiphoton and tunneling ionization regimes. These findings have wide implications for strong-field atomic physics and providing new possibilities for quantum local realism tests.

We study the relaxation dynamics of temperature anisotropy between longitudinal and transverse motions of ${}^{87}\mathrm{Rb}$ atoms in a one-dimensional optical lattice. The temperature imbalance is established by Raman sideband cooling applied along the lattice axis. At low temperature, a large difference between the longitudinal and transverse vibration frequencies limits the relaxation. We transform the trap potential by phase modulating the lattice beam to reduce the anisotropy and thereby enhance cross-dimensional sympathetic cooling. An extension of classical theory, which incorporates the quantization of the atomic motion, explains the experimental results well. We also report that effects of trap anharmonicity and atomic vector polarizability on broadening of the Raman sideband cancel each other at a particular lattice depth, which greatly facilitates sideband cooling.

The temporal-mode (TM) basis is a prime candidate to perform high-dimensional quantum encoding. Quantum frequency conversion has been employed as a tool to perform tomographic analysis and manipulation of ultrafast states of quantum light necessary to implement a TM-based encoding protocol. While demultiplexing of such states of light has been demonstrated in the quantum pulse gate (QPG), a multiplexing device is needed to complete an experimental framework for TM encoding. In this work we demonstrate the reverse process of the QPG. A dispersion-engineered difference frequency generation in nonlinear optical waveguides is employed to imprint the pulse shape of the pump pulse onto the output. We study experimentally the process by spectrally shaping the first five orders of Hermite-Gauss modes of various bandwidths. Finally, we establish and model the limits of practical, reliable spectral pulse shaping operation.

Transient phenomena of phase-modulated cutoff wave packets are explored by deriving an exact general solution to Schrödinger's equation for finite-range potentials involving arbitrary initial quantum states. We show that the dynamical features of the probability density are governed by a virtual self-induced two-level system with energies $E_{+}$ and $E_{-}$ due to the phase modulation of the initial state. The asymptotic probability density exhibits Rabi oscillations characterized by the frequency $\mathrm{\Omega }=(E_{+}-E_{-})/\hslash$, which are independent of the potential profile. It is also found that for a system with a bound state, the interplay between the virtual levels with the latter causes a quantum beat effect with a beating frequency, $\mathrm{\Omega }$. We also find a regime characterized by a time-diffraction phenomenon that allows us to measure unambiguously the delay time, which can be described by an exact analytical formula. It is found that the delay time agrees with the phase time only for the case of strictly monochromatic waves.